sensors
Article Analysis of the Influence of the Vortex Shedder Shape on the Metrological Properties of the Vortex Flow Meter
Mariusz R. Rzasa 1,* and Beata Czapla-Nielacna 2
1 Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Proszkowska 76 Street, 45-758 Opole, Poland 2 Faculty of Mechanical Engineering, Opole University of Technology, Mikolajczyka 5 Street, 45-271 Opole, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-602-345-162
Abstract: Vortex flow meters are used to measure the flow of gases and liquids. The flow meters of this type measure the frequency of vortices that arise behind an obstacle set in the path of the flowing fluid. The frequency is a function of the speed of the flowing fluid. This obstacle is called the vortex shedder bar. The advantage of this solution is that the frequency of vortices does not viscose on the rheological properties of the fluid, such as viscosity or density. As a result, the indications of the vortex flowmeter do not depend on the temperature and type of fluid. The work includes numerical and experimental studies of the effect of changing the shape of a vortex generator on the stability of vortex generation in a vortex flowmeter. The article presents a numerical analysis of the influence of selected surfaces of the vortex shedder on the parameters of the vortex flowmeter. In order to determine the influence of the shape of the vortex shedder on the type of generated vortices,
simulations were carried out for various flow velocities. Numerical calculations were experimentally verified for a cylinder-shaped vortex shedder. The experimental tests consist in determining the
Citation: Rzasa, M.R.; velocity field behind the vortex shedder. For this purpose, a proprietary method of determining local Czapla-Nielacna, B. Analysis of the liquid velocities and the visualization of local vortices were used. On the basis of the conducted Influence of the Vortex Shedder Shape research, the influence of the shape of the vortex shedder on the width of the von Karman vortex on the Metrological Properties of the street was determined and the optimal longitudinal distance from the shedder was determined in Vortex Flow Meter. Sensors 2021, 21, which it is most useful to measure the frequency of the vortices. This place ensures the stability of the 4697. https://doi.org/10.3390/ frequency of the generated vortices. s21144697 Keywords: vortex flow meter; flow visualization; flow measurement; flow visualization Academic Editor: Giovanni Betta
Received: 10 June 2021 Accepted: 7 July 2021 1. Introduction Published: 9 July 2021 One of the solutions used to measure the velocity of liquids are vortex flow meters. These flow meters are used to measure the velocity of liquids of various densities and Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in viscosities. Their advantage is that the measurement result is not significantly influenced by published maps and institutional affil- solid particles carried with the liquid. They can therefore be used to measure contaminated iations. liquids. A second advantage is the very low pressure drop across the measuring device. Their disadvantage is the relatively small measuring range [1]. The principle of operation of the vortex flowmeter is to create regular vortices behind the generator placed in the flowing liquid. The frequency of the vortices is a function of the flow velocity. The vortex generator can have different shapes. This shape has a direct Copyright: © 2021 by the authors. impact on the sensitivity and measuring range of the flowmeter. The frequency of the Licensee MDPI, Basel, Switzerland. This article is an open access article resulting vortices is a measure of the flow velocity, which is expressed by the Strouhal distributed under the terms and number [2]: f ·d conditions of the Creative Commons St = , (1) Attribution (CC BY) license (https:// v creativecommons.org/licenses/by/ where: St—Strouhal number, f —frequency of vortices, d—characteristic dimension, v— 4.0/). flow velocity.
Sensors 2021, 21, 4697. https://doi.org/10.3390/s21144697 https://www.mdpi.com/journal/sensors Sensors 2021, 21, x FOR PEER REVIEW 2 of 22
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where: St—Strouhal number, f—frequency of vortices, d—characteristic dimension, v— flow velocity. The Strouhal number is constant regardless of the velocity of the liquid that passes The Strouhal number is constant regardless of the velocity of the liquid that passes the vortex generator. The advantage of this solution is that the frequency of the generated the vortex generator. The advantage of this solution is that the frequency of the generated von Karman vortices does not depend on the rheological properties of the fluid, such as von Karman vortices does not depend on the rheological properties of the fluid, such as viscosity or density. As a result, the indications of the vortex flowmeter do not depend on viscosity or density. As a result, the indications of the vortex flowmeter do not depend on the temperature and type of fluid. the temperature and type of fluid. It should be noted, however, that the von Karman vortex path arises for the turbulen It should be noted, however, that the von Karman vortex path arises for the turbulen flow. Thus, the Reynolds number should be greater than 5000 [3]. Therefore, the size of flow. Thus, the Reynolds number should be greater than 5000 [3]. Therefore, the size of the vortex shedder bar should be adapted to the rheological properties of the liquid and the vortex shedder bar should be adapted to the rheological properties of the liquid and the measuring range. The rheological properties of the fluid depend on the type of fluid, the measuringtemperature range. and The its physicochemical rheological properties composition. of the fluid Moreover, depend the on presence the type of of a significantfluid, temperatureamount and of solid its physicochemical particles in a liquid composition. significantly Moreover, changes the itspresence rheological of a significant properties [4]. amountWhen of solid selecting particles the diameterin a liquid of significantly the vortex shedder, changes the its valuerheological of the properties Reynolds [4]. number Whencalculated selecting fromthe diameter the formula of the should vortex be considered.shedder, the value of the Reynolds number calculated from the formula should be considered. v·dρ Re = ⋅ , (2) 𝑅𝑒 = , (2) µ where:where: ρ—densityρ—density of the of fluid, the fluid, μ—dynamicµ—dynamic viscosity viscosity of the of fluid. the fluid. In thisIn work, this work, tests tests were were carried carried out out for for pure pure water water at at a a temperature temperature of 2020 ◦°CCin in the the speed speedrange range from from 0.5 0.5 to to 2 2 m/s. m/s. Assuming Assuming a a vo vortexrtex generator generator size size of of 20 20 mm, mm, Reynolds Reynolds num- numbers bers areare between between 10,000 10,000 and and 40,000. 40,000. Thus, Thus, this this is is sufficient sufficient to to produce produce a avon von Karman Karman street. street. FigureFigure 1 shows1 shows a typical a typical design design of a flowmeter of a flowmeter [5]. It [ 5consists]. It consists of a vortex of a vortex generator, generator, whichwhich is mounted is mounted in the inflow the space. flow It space. causes It vortices causes to vortices form behind to form it, behindcreating it, the creating char- the acteristiccharacteristic von Karman von vortex Karman path. vortex In order path. to In measure order to the measure frequency the frequency of the vortices of the that vortices arise,that a pressure arise, adetector pressure is detectormounted isat mounteda certain distance. at a certain The distance. simplest solution The simplest is a pres- solution sure sensoris a pressure with high sensor measurement with high measurementdynamics. The dynamics. frequency Theof the frequency vortices is of measured the vortices is electronically.measured electronically.
Vortex detector
Shedder bar
FigureFigure 1. Vortex 1. Vortex flowmeter. flowmeter.
The shapeThe shape of the of vortex the vortex sheder sheder has a has signifi a significantcant impact impact on the on theparameters parameters and and met- metro- rologicallogical properties properties of the of theflow flow meter meter [6]. [Its6]. shape Its shape should should ensure ensure the formation the formation of regular of regular vorticesvortices in the in largest the largest possible possible measuring measuring range. range. The most The mostcommon common shape shape is a cylinder. is a cylinder. ThereThere are many are many works works on this on subject this subject in the in lit theerature literature [1,7]. [Classic1,7]. Classic designs designs of vortex of vortex flow flow metersmeters are also are used also usedin two-phase in two-phase flows flows [8]. [The8]. Theresearch research in this in this paper paper will will be becompared compared to to a cylinder-shapeda cylinder-shaped shedder shedder bar. bar. The The main main di disadvantagesadvantage of of the the cylindrical cylindrical shape shape is its very very narrow measuring rangerange [[9].9]. Therefore,Therefore, therethere is is a a need need to to look look for for other other solutions solutions [2 [2].]. There Thereare are many many works works in in the the literatureliterature whichwhich describedescribe cylindricalcylindrical shedder bar [1,7,10]. [1,7,10]. In In this this paper,paper, this shape willwill bebe usedused as as a a reference reference in in the the assessment assessment of theof the influence influence of selected of selectedshedder shedder surfaces surfaces on the on vonthe Karmanvon Karman vortex vortex path. path. The mainThe main disadvantage disadvantage of the of cylindrical the cylindricalshape shape is its narrow is its narrow measuring measuring range rang duee to due the to stability the stability of the of generated the generated vortices vor- [7]. As tices the[7]. sizeAs the and size shape and of shape the vortex of the generatorvortex generator has a large has impacta large onimpact the correct on the operationcorrect of operationthe vortex of the flowmetervortex flowmeter [2,11], the [2,11], search the forsearch new for solutions new solutions is still justifiedis still justified [9,12], [9,12], despite the fact that many shapes of vortex generators are known. despite the fact that many shapes of vortex generators are known. Many vortex shedder bars solutions are used in commercial flow meters. Many vortex generator solutions are used in commercial flow meters. Despite so many solutions, no
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Many vortex shedder bars solutions are used in commercial flow meters. Many vor- tex generator solutions are used in commercial flow meters. Despite so many solutions, nouniversal universal shape shape of theof the vortex vortex shedder shedder bar bar has has been been developed. developed. This This study study is devotedis devoted to tothe the analysis analysis of of the the influence influence of of selected selected surfaces surfaces of of the the vortex vortex sheddershedder barbar onon selectedselected parameters of the vortex flowme flowmeter.ter. In the firstfirst part, numericalnumerical tests were carried out, the aim of which was to distinguish significantsignificant su surfacesrfaces of the vortex generator, which may have a a significant significant impact impact on on the the metrological metrological parameters parameters of ofthe the flow flow meter. meter. Then, Then, the these- lectedselected shapes shapes were were tested tested experimentally. experimentally. A cylinder withwith aa diameterdiameter of ofd d= = 20 20 mm mm was was adopted adopted as as the the reference reference shape shape (Figure (Figure2 ). 2).Eight Eight surfaces surfaces were were distinguished distinguished in the in cross-section.the cross-section. Four Four of them of them form form the rakethe rake face face and andthe remainingthe remaining four four form form the trailingthe trailing face. face.
Figure 2. The basic vortex shedder shape.
This solution can be used to measure the fl flowow of clean and contaminated fluidsfluids with solid particles. Measurement error of the currentcurrent valuevalue ofof thethe streamstream 0.50.5÷ ÷ 1% for liquids and approx. approx. 2% 2% for for gases. gases. The The measurement measurement erro errorr is significantly is significantly influenced influenced by the by regu- the larityregularity of the of vortices the vortices formed. formed. The Thecomplex complex nature nature of the of theresulting resulting chips chips provides provides a lot a lotof informationof information about about the the process process of of their their formation. formation. This This information information can can be be processed on the basis of data fusing process [[13].13]. In order to determine the influenceinfluence of individual surfaces on thethe vonvon KarmanKarman swirlswirl pathway formed behind the vortex shedder bar.bar. The main analysis was the influenceinfluence of individual surfaces on the stability of the generated vortices. The results of the calculations were compared to the calculationscalculations for thethe cylinder-shapedcylinder-shaped generator.generator. The research was carried out in such a way that selected surfaces from 1 to 8 were modifiedmodified (Figure2 2)) andand then numerical calculations were were carried carried out out for for the the same same conditions conditions as as for for the the cylinder. cylinder. Shapes with a modifiedmodified rake face were proposed (Figure3 3a).a). TheThe secondsecond modificationmodification isis the changes in the runoffrunoff surfacesurface (Figure(Figure3 3b).b). TheThesame samecharacteristic characteristic dimensiondimension dd= = 2020 mm was kept in all modifications. modifications. In addition, the effect of extending the dimension of the sherdder bar in the direction of flow motion was tested (Figure3c). The elongation was sherdder bar in the direction of flow motion was tested (Figure 3c). The elongation was 6 6 mm (W1) and 12 mm (W2). In addition, it was checked what effect is the use of a slot mm (W1) and 12 mm (W2). In addition, it was checked what effect is the use of a slot with with a radius of 3 mm (W3) and a slot with a radius of 6 mm (W4) on the lower and upper a radius of 3 mm (W3) and a slot with a radius of 6 mm (W4) on the lower and upper surfaces of the shedder bar. surfaces of the shedder bar. The aim of the work is to present the influence of changes in the shape of the rake and runoff surface in the vortex shedder bar on the stability of the vortices. The work carried out numerical and experimental tests on the basis of which the parameters for various shapes of vortex shedder bar were determined.
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FigureFigure 3. 3.Shapes Shapes resulting resulting fromfrom (a) rake surface surface modification modification (b (b) )runoff runoff surface surface modification modification (c) (oval.c) oval.
2. NumericalThe aim Methodof the work is to present the influence of changes in the shape of the rake and Manyrunoff mathematicalsurface in the models vortex areshedder evaluated bar on to the simulate stability flow of velocity.the vortices. The mostThe work popular modelscarried forout modeling numerical complex and experimental flow problems tests areon numericalthe basis of methods which the CFD parameters (Computational for Fluidvarious Dynamics). shapes of vortex These shedder models arebar mainlywere determined. based on Reynolds theory. It is assumed that fluid motion can be defined by two parameters such as average velocity and fluctuation ve- locity.2. Numerical As a result, Method the Navier–Stokes equation describing the motion of a fluid additionally containsMany a turbulencemathematical stress models tensor are [evaluated12]. This causesto simulate additional flow velocity. variables The to most appear popu- in the equation.lar models On for correctness modeling complex of the numerical flow problems results are affects numerical using me suitablethods CFD turbulence (Computa- model andtional preparation Fluid Dynamics). right preprocessing These models are parameters. mainly based To someon Reynolds of themost theory. important It is assumed aspects includethat fluid the motion number can ofbe meshdefined elements by two parameters and the areas such of as its average density. velocity Conducted and fluctua- research purposetion velocity. the selection As a result, of the the Navier–Stokes optimal turbulence equation model describing and to the determine motion of thea fluid minimum ad- numberditionally of contains the mesh a elements.turbulence stress tensor [12]. This causes additional variables to ap- pearThe in the appearance equation. On of additionalcorrectness variablesof the numerical in the Reynoldsresults affects equations using suitable requires turbu- supple- mentinglence model the matamaticand preparation model right with preprocess additionaling equations. parameters. In practice,To some theyof the are most most im- often knownportant asaspects k-ε or include k-ω turbulence the number models of mesh [12 ,elements14]. Each and of thesethe areas models of its has density. certain Con- limita- tions.ducted They research make purpose each of the them selection reflect of the the real optimal movement turbulence of fluids model better and orto determine worse. In the firstthe minimum part of the number work, researchof the mesh was elements. carried out to identify the model that best reproduces the realThe shape appearance of the vonof additional Karman vortexvariables path. in the Reynolds equations requires supple- mentingThe the k-ε matamaticmodel takes model into with account additional the relationshipequations. In betweenpractice, they the vorticityare most often and the kineticknown energyas k-ε or of k- turbulenceω turbulence [14 ].models This model[12,14]. models Each of well these turbulence models has in certain free flow limita- and in sheartions. layers.They make It is each characterized of them reflect by low thesensitivity real movement to boundary of fluids better conditions, or worse. especially In the to thefirst distribution part of the work, of liquid research velocity was carried at the inletout to to identify the channel. the model This that is abest desirable reproduces feature the real shape of the von Karman vortex path. due to the fact that these quantities are often not exactly known in practical calculations. The k-ε model takes into account the relationship between the vorticity and the ki- Meanwhile, the k-ω model takes into account both the kinetic energy of turbulence and netic energy of turbulence [14]. This model models well turbulence in free flow and in the speed of energy dissipation in its solution. In the k-ω model, like in k-ε, k will express shear layers. It is characterized by low sensitivity to boundary conditions, especially to the kinetic energy of turbulence and ω is the ratio of the energy dissipation speed ε to the distribution of liquid velocity at the inlet to the channel. This is a desirable feature due the kinetic energy k. The k-ω model, on the other hand, models the turbulent flow in the to the fact that these quantities are often not exactly known in practical calculations. Mean- boundarywhile, the layerk-ω model much better,takes into while account it is very both sensitive the kinetic tothe energy values of ofturbulence turbulent and quantities the inspeed free flow.of energy dissipation in its solution. In the k-ω model, like in k-ε, k will express the kineticIt was energy found of turbulence that you can and combine ω is the the ratio desired of the features energy ofdissipation both models speed by ε combining to the themkinetic into energy a single k. The model, k-ω model, in ANSYS on the Fluent other it washand, named models k- theω SST. turbulent The k- flowω SST in modelthe wasboundary used for layer further much numerical better, while research. it is very This sensitive model to is the a good values representation of turbulent quantities of the kinetic energyin free flow. of the vortices forming. The appropriate selection of the finite element mesh has a significant impact on the simulation results [15]. The structural computational mesh was generated for rectangular
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It was found that you can combine the desired features of both models by combining It was found that you can combine the desired features of both models by combining them into a single model, in ANSYS Fluent it was named k-ω SST. The k-ω SST model them into a single model, in ANSYS Fluent it was named k-ω SST. The k-ω SST model was used for further numerical research. This model is a good representation of the kinetic Sensors 2021, 21, 4697 was used for further numerical research. This model is a good representation of the kinetic5 of 20 energy of the vortices forming. energy of the vortices forming. The appropriate selection of the finite element mesh has a significant impact on the The appropriate selection of the finite element mesh has a significant impact on the simulation results [15]. The structural computational mesh was generated for rectangular simulation results [15]. The structural computational mesh was generated for rectangular elementselements ofof variousvarious shapes and and sizes. sizes. The The mesh mesh is isrefined refined in inthe the immediate immediate vicinity vicinity of the of elements of various shapes and sizes. The mesh is refined in the immediate vicinity of the thevortex vortex shedder shedder bar bar (Figure (Figure 4).4). For For the the purpos purposeses of of the research, aa calculationcalculation grid grid was was vortex shedder bar (Figure 4). For the purposes of the research, a calculation grid was preparedprepared for for a a rectangular rectangular duct duct with with a a length length of of L1 L1 = = 900 900 mm mm and and a a widthwidth of of L2L2 == 600600 mm.mm. prepared for a rectangular duct with a length of L1 = 900 mm and a width of L2 = 600 mm. AA cylindercylinder withwith aa diameter diameter of of 20 20 mm mm was was placed placed in in the the middle middle of of the the channel. channel. The The width width A cylinder with a diameter of 20 mm was placed in the middle of the channel. The width ofof thethe channelchannel isis soso largelarge thatthat thethe influenceinfluence ofofthe the side side walls walls of of the the channel channel on on the the process process of the channel is so large that the influence of the side walls of the channel on the process ofof vortexvortex formationformation cancan bebe neglected.neglected. of vortex formation can be neglected.
Figure 4. Computational mesh. FigureFigure 4. 4.Computational Computational mesh. mesh. Figure 5 presents the results of numerical simulation of the number of mesh of finite FigureFigure5 5presents presents the the results results of of numerical numerical simulation simulation of of the the number number of of mesh mesh of of finite finite 400,848 nodes. The k-ω SST model for a cylinder-shaped of shedder bar is a good repre- 400,848400,848 nodes.nodes. TheThe k-ω SST model for for a a cylinder-shaped cylinder-shaped of of shedder shedder bar bar is is a agood good repre- rep- sentation of the von Karman street, so it can be used in the study of shedder bars of other resentationsentation of of the the von von Karman Karman street, street, so soit can it can be used be used in the in thestudy study of shedder of shedder bars barsof other of shapes. othershapes. shapes.
Figure 5. The results of numerical calculations for the k-ω model used in the further part of the Figure 5. The results of numerical calculations for the k-ω model used in the further part of the Figurework. 5. The results of numerical calculations for the k-ω model used in the further part of the work. work. 3. Computational Results 3. Computational Results 3. ComputationalIn order to investigate Results the influence of the shape of the vortex generator on the stability In order to investigate the influence of the shape of the vortex generator on the sta- of theIn generated order to vortices,investigate simulations the influence were of carried the shape out for of variousthe vortex flow generator velocities on (0.5 the m/s, sta- bility of the generated vortices, simulations were carried out for various flow velocities 1bility m/s, of 2 m/s).the generated Numerical vortices, calculations simulations were performed were carried with out the for ANSYS various Fluent flow software.velocities (0.5 m/s, 1 m/s, 2 m/s). Numerical calculations were performed with the ANSYS Fluent The(0.5 calculations m/s, 1 m/s, were2 m/s). carried Numerical out on calculations a computing were server performed consisting with of two the computers. ANSYS Fluent The software. The calculations were carried out on a computing server consisting of two com- firstsoftware. had 24 The cores calculations and the second were carried had 20 out cores on Ina computing numerical calculations,server consisting the Turbulenceof two com- puters. The first had 24 cores and the second had 20 cores In numerical calculations, the k-STputers. SST The model first was had used 24 cores for a and two-dimensional the second had velocity 20 cores field In andnumerical a non-stationary calculations, flow. the Turbulence k-ST SST model was used for a two-dimensional velocity field and a non-sta- TheTurbulence boundary k-ST conditions SST model were was the used assumption for a tw thato-dimensional there is a uniform velocity velocity field and distribution a non-sta- tionary flow. The boundary conditions were the assumption that there is a uniform veloc- intionary the inflow flow. channel The boundary and that conditions the liquid were flowing the inassumption the channel that is there water. is a uniform veloc- ity distribution in the inflow channel and that the liquid flowing in the channel is water. ity distributionThe calculation in the results inflow were channel compared and that with the the liquid results flowing for the in cylinder-shaped the channel is water. gener- ator. For the digital genaric vortex, regular and stable vortices were obtained for a liquid flow velocity of 0.5 m/s, 1 m/s and 2 m/s. The results of the numerical calculations are presented in Table1. The frequency of the generated vortices was determined on the basis of how the pressure changed at the selected point on the basis of successive time steps.
The calculation results for other shapes of shedder bars will be compared to the values presented in Table1. Sensors 2021, 21, 4697 6 of 20
Table 1. Computational results for the vortex shedder from the Figure2.
v [m/s] f [Hz] ∆p [Pa] 0.5 6.01 128.11 1 12.44 442.51 2 26.32 1529.5
The main objective of the numerical research was to determine the effect of individual surfaces of the shedder bar on the frequency, pressure and stability of vortex formation. These are the parameters that have a direct impact on the proper operation of the vortex flowmeter. The range of changes in the frequency of the generated vortices affects the sensitivity of the flowmeter. Figure6 shows the numerical results of comparing the values of frequency changes of the vortices formed for various modifications of the vortex generator. The designations of the Sensors 2021, 21, x FOR PEER REVIEW 7 of 22 shapes correspond to the markings in Figure2. The values in the diagram represent the ratio of the frequency of vortices generated by individual shapes to the reference frequency f0 (Table1).
FigureFigure 6. Shapes6. Shapes resulting resulting from from (a ()a) rake rake surface surface modificationmodification (b) runoff surface surface modification modification (c ()c oval.) oval.
The more the f/f0 ratio differs from 1, the greater the impact on the sensitivity of the flowmeter will be the modification of the surface areas consistent with the markings in Figure 6. As it results from Figure 6a, the greatest impact on the sensitivity of the vortex flowmeter is the modification of areas 1 and 3 together with areas 2 and 4. In this type, the greatest variations are obtained for different flow velocity, but the variations are non-lin- ear. Modifying only areas 3 and 4 or 1 and 2 does not bring such good results. The modi- fications to the P3 and P4 deserve special attention here In the case of the runoff surface modification, a significant improvement in the flow- meter sensitivity is obtained for the shapes T2 and T7. These shapes have a sharp edge, which makes it easier to detach the vortices. Modification of the upper and lower flow surfaces of the vortex shedder bar (shapes in Figure 6c) mainly increases the frequency of the generated vortices, but does not signif- icantly affect the sensitivity of the flowmeter. Only the modification of W3 has a visible effect on the sensitivity.
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The more the f/f0 ratio differs from 1, the greater the impact on the sensitivity of the flowmeter will be the modification of the surface areas consistent with the markings in Figure6. As it results from Figure6a, the greatest impact on the sensitivity of the vortex flowmeter is the modification of areas 1 and 3 together with areas 2 and 4. In this type, the greatest variations are obtained for different flow velocity, but the variations are non-linear. Modifying only areas 3 and 4 or 1 and 2 does not bring such good results. The modifications to the P3 and P4 deserve special attention here In the case of the runoff surface modification, a significant improvement in the flowme- ter sensitivity is obtained for the shapes T2 and T7. These shapes have a sharp edge, which makes it easier to detach the vortices. Modification of the upper and lower flow surfaces of the vortex shedder bar (shapes in Figure6c) mainly increases the frequency of the generated vortices, but does not signif- icantly affect the sensitivity of the flowmeter. Only the modification of W3 has a visible effect on the sensitivity. The second important parameter influencing the operation of the vortex flowmeter is the value of pressure changes of the generated vortices. The greater the pressure change of the generated vortices, the greater the signal-to-noise ratio in the measurement signal. Figure7 shows the results of the numerical simulation. These results show the impact of modification of the rake and trailing surface on pressure changes generated by vortices formed behind individual shedder bars. The greatest changes for different fluid streams are obtained for modifications P3 and P4 (Figure7a) and for modifications T1 and T2 (Figure7b). The least effect is obtained for the T7 modification. On the other hand, for the W1 modification, the changes increase with small flow rate, while for larger flows they remain at the same level. Modification of W3 lowers the level by approximately a constant amount. Based on the research, it was found that the modification of the rake surface, consisting in increasing the drag coefficient, causes an increase in the pressure difference behind the vortex generator. This improves the signal-to-noise properties of the flowmeter, but the processing characteristics become more non-linear. This will make a difference at higher fluid flow rates. The stability of the von Karman street has a great influence on the correct work of the vortex flowmeter. Further research was carried out to determine the impact of changes in the shape of rake surface on the stability of vortex street. Modifications of the shape of shedder bar P3, P4, T1, T2, T7, W1 and W3 were selected for further numerical tests. The results of the analysis for the shapes P3 and P4 are shown in Figure8. Modification of the rake surface destabilizes the vortex street in a wide range of velocity of the tested fluid. The destabilization of the vortex street is already noticeable for a very low velocities of flow velocity v = 0.5 m/s (Figure8a,b). Even a gentle flattening of the rake face of the vortex sedder bar causes considerable disturbance to the formation of the vortex street. Modification P4 may be appropriate for very low flow rates as it generates the greatest amplification of the pressure amplitude downstream of the vortex generator. Moreover, it extends the measuring range. The analysis shows that in order to obtain good stability of the generated vortices, it is best if the rake surface is as streamlined as possible. It will be a good solution especially for measuring high velocities of flowing fluid. Analyzing the obtained results for the shapes in which the runoff surfaces T1 and T2 were modified (Figure9a,b), it was found that the modification of these surfaces did not destabilize the stream. The reason is that the stream of flowing liquid mainly breaks off from the top and bottom surfaces of the shedder bar. These modifications advantageously affect the amplitude of pressure changes of the resulting vortices. The T7 modification (Figure9e,f) has an even smaller impact on the stability of the von Karman swirl path. Since Modification T7 has little effect on improving the value of the pressure amplitude of the resulting vortices, it is advisable to pay special attention only to the modification T2. Sensors 2021, 21, 4697 8 of 20 Sensors 2021, 21, x FOR PEER REVIEW 8 of 22
The streamlined shape of the rake surface has a positive effect on the stabilization Theof the second vortex streetimportant for high parameter flow velocities. influencing Sharp ending the of operation the trailing of surface the vortex does not flowmeter is thedestabilize value of pressure the vortex changes street, but of improves the generated the sensitivity vortices. of the The vortex greater flowmeter. the pressure Thus, it change has a positive effect on improving the parameters of the vortex flowmeter. To increase. The of themodification generated of vortices, W3 does notthe significantlygreater the change signal-to-noise the parameters ratio of thein the vortex measurement flowmeter; signal. Figurehowever, 7 shows it linearizes the results its characteristics. of the numerical Based onsimulation. this analysis, These for experimental results show research, the impact of modificationit was decided of the to rake develop and the trailing shapes surface of vortex on generators pressure which changes constitute generated a kind ofby vortices formedcompilation behind individual of the modifications shedder presented bars. in Figure2. Figure 10 shows the proposed shapes of vortex shedder bars that have been subjected to experimental tests.
Figure 7.Figure Shapes 7. Shapes resulting resulting from from (a) (rakea) rake surface surface modification modification (b )(b runoff) runoff surface surface modification modification (c) oval. (c) oval.
The greatest changes for different fluid streams are obtained for modifications P3 and P4 (Figure 7a) and for modifications T1 and T2 (Figure 7b). The least effect is obtained for the T7 modification. On the other hand, for the W1 modification, the changes increase with small flow rate, while for larger flows they remain at the same level. Modification of W3 lowers the level by approximately a constant amount. Based on the research, it was found that the modification of the rake surface, consist- ing in increasing the drag coefficient, causes an increase in the pressure difference behind the vortex generator. This improves the signal-to-noise properties of the flowmeter, but the processing characteristics become more non-linear. This will make a difference at higher fluid flow rates.
Sensors 2021, 21, 4697 9 of 20 Sensors 2021, 21, x FOR PEER REVIEW 10 of 22
FigureSensors 8. TheFigure 2021 influence, 21 8., x The FOR influence PEER of 1, REVIEW 2, of 3 and1, 2, 3 4 and surfaces 4 surfaces modification modification onon regularity of ofgenerated generated vortices vortices for (a) P3 for with (a) v P3 = 0.5 with m/s,11 v =of 0.522 m/s, (b) P3 with v = 2 m/s, (c) P4 with v = 0.5 m/s, (d) P4 with v = 2 m/s. (b) P3 with v = 2 m/s, (c) P4 with v = 0.5 m/s, (d) P4 with v = 2 m/s.
Figure 9. TheFigure influence 9. The influence of 5,6,7 of and 5,6,78 and surfaces 8 surfaces modification modification onon regularity of ofgenerated generated vortices vortices for (a) forT1 with (a) T1v = with0.5 m/s, v = 0.5 m/s, (b) T1 with(b v) T1 = 2with m/s, v = (2c )m/s, T2 ( withc) T2 with v = 0.5v = 0.5 m/s, m/s, (d (d)) T2 T2 withwith v v = =2 m/s, 2 m/s, (e) T2 (e )with T2 v with = 0.5v m/s, = 0.5 (f) T2 m/s, with (f v) = T2 2 m/s. with v = 2 m/s.
Figure 10. Experimental shapes of vortex shedder bars.
4. Test Stand for Experimental Research In order to verify the numerical calculations and determine the influence of the di- mensions and shapes of the vortex shedder bar on the characteristic dimensions related to the construction of vortex flow meters, a test stand was built and a measurement method was developed to enable the visualization of vortex’s arising behind the shedder. In order to visualize the vortex path, the marker method was used [16]. This method enables the measurement of the local velocity of fluid movement and the tracing of eddies that occur. The selection of tags has a great influence on the results of the visualization.
Sensors 2021, 21, x FOR PEER REVIEW 11 of 22
Sensors 2021, 21, 4697 10 of 20
Figure 9. The influence of 5,6,7 and 8 surfaces modification on regularity of generated vortices for (a) T1 with v = 0.5 m/s, (b) T1 with v = 2 m/s, (c) T2 with v = 0.5 m/s, (d) T2 with v = 2 m/s, (e) T2 with v = 0.5 m/s, (f) T2 with v = 2 m/s.
FigureFigure 10. ExperimentalExperimental shapes shapes of of vortex shedder bars. 4. Test Stand for Experimental Research 4. Test Stand for Experimental Research In order to verify the numerical calculations and determine the influence of the In order to verify the numerical calculations and determine the influence of the di- dimensions and shapes of the vortex shedder bar on the characteristic dimensions related mensions and shapes of the vortex shedder bar on the characteristic dimensions related to the construction of vortex flow meters, a test stand was built and a measurement method to the construction of vortex flow meters, a test stand was built and a measurement was developed to enable the visualization of vortex’s arising behind the shedder. Sensors 2021, 21, x FOR PEER REVIEWmethod was developed to enable the visualization of vortex’s arising behind the shedder.12 of 22 In order to visualize the vortex path, the marker method was used [16]. This method In order to visualize the vortex path, the marker method was used [16]. This method enables the measurement of the local velocity of fluid movement and the tracing of eddies enables the measurement of the local velocity of fluid movement and the tracing of eddies that occur. The selection of tags has a great influence on the results of the visualization. thatThey occur. should The be selection of an appropriate of tags has size a greatand the influence material on from the whichresults they of the are visualization. made should They should be of an appropriate size and the material from which they are made should have a density similar to that of the fluid. These markers should not significantly interfere have a density similar to that of the fluid. These markers should not significantly interfere with fluid movement. Water with polyamide markers with a density of 940 kg/m3 and with fluid movement. Water with polyamide markers with a density of 940 kg/m3 and granulation from 20 µμmm toto 11 mmmm waswas usedused forfor thethe experimentalexperimental tests.tests. TheThe markersmarkers hadhad aa good reflectivereflective surface.surface. The measurement method presented in this article is similar to the PIV. However,However, itit differs inin thethe methodmethod ofof calculating calculating the the local local speed speed value. value. This This method method consists consists in in register- regis- ingtering the the trajectory trajectory of theof the movement movement of markers of markers moving moving with with the liquid.the liquid. Compared Compared to the to PIVthe PIV method, method, the tagsthe tags have have much much larger larger dimensions. dimensions. This kindThis low-costkind low-cost DPIV set-ups,DPIV set-ups, using freeusing PIV free software PIV software and high-speed and high-speed cameras cameras instead ofinstead the classical of the classical double exposure double exposure cameras, havecameras, been have successfully been successfully employed inemployed PIV and liquid-granularin PIV and liquid-granular PIV applications PIV [applications17–19]. The basis[17–19]. for The calculating basis for the calculating speed of movement the speed of of the movement tag is the analysisof the tag of is its the movement analysis based of its onmovement the image based of only on the one image image of ofonly the one fluid imag flow.e of This the fluid method flow. does This not method require does image not correlationrequire image of atcorrelation least two of consecutive at least two photos, consecutive as is the photos, case withas is thethe PIVcase method.with the ThePIV imagemethod. of The a moving image particle of a moving is recorded particle with is recorded a long exposure. with a long The exposureexposure. time The isexposure so long thattime theis so marker long that in the the imagemarker is in visible the image in the is form visible of in a longitudinal the form of a streak longitudinal with a shapestreak correspondingwith a shape corresponding to the marker to movement the marker trajectory. movement trajectory. The local liquid velocity is determineddetermined on the basisbasis ofof thethe tracestraces leftleft byby thethe markersmarkers (Figure(Figure 1111).). AfterAfter hittinghitting the the marker, marker, the the light light that that shines shines through through the the measurement measurement section sec- istion reflected is reflected from from its surface. its surface. In cameos In cameos it is visible it is visible as a bright as a bright spot. Whenspot. When a long a exposure long ex- timeposure is used,time is the used, trace the of trace the moving of the moving marker marker will be visiblewill be as visible a bright as a line. bright line.
FigureFigure 11.11. ImageImage ofof tracertracer particleparticle flow.flow.
The length of the trace left by the marker in the image is the basis for calculating the local velocity and direction of movement of the fluid. The local speed is calculated from the formula: